Modified Mohr-Coulomb Fracture Model Research Articles

Prediction of edge fracture during hole-flanging of advanced high-strength steel considering blanking pre-damage

The stretch-flangeability of advanced high-strength steel (AHSS) sheets after blanking highly depends on the stress states as well as the edge pre-damage inherited from the initial blanking process. It cannot be predicted by using conventional forming limit diagram methods. To solve this issue, in this study, a numerical simulation model of the two-step hole cutting-hole expansion tests for the TRIP800 sheet was established by considering the initial surface irregularities induced by hole fabrication into the hole expansion process. Two methods, punching and wire-cut electrical discharge machining with low speed were adopted to cut holes. The modified Mohr–Coulomb fracture model together with post-failure softening was utilized to predict the fracture initiation and crack propagation during two forming processes. The results manifested that the WEDM-LS cutting method brought negligible damage to the hole edge and the sheet edge fabricated by this method can be assumed without pre-damage. Multiple finer notches were detected at the surface of the punched hole. These features triggered stress states with higher stress triaxiality up to 0.6 and thus accelerated the edge fracture occurrence during the hole expansion deformation. The measured hole expansion ratio of the punched hole was 26.1%, which was correctly predicted by the proposed model by considering edge pre-damage. As a comparison, the ideal model without pre-damage overestimated the value by about 100%.

Prediction the stainless steel sheet fracture with mesh size effect for shell elements

The application of ductile fracture criteria to shell elements yields invalid after the onset of necking and sensitivity to element size. The mesh-size regularisation strain study indicates that fracture strain modified with element dimension results in the same stress state. This phenomenon can't be accurately explained by current strain based fracture models. To fill this gap, this paper proposed that the fracture stress threshold σf for the Mohr-Coulomb criterion can be assumed to be an element dimension effect function of the form: σf (le)∝le−m. It follows then that the Modified Mohr-Coulomb fracture model and post-initiation damage are related to the element size by stress concentration exponent m. A plasticity and fracture testing program is performed on 1 mm thick 301L steel sheets to test this hypothesis. The Arcan-type tests were employed to calibrate parameters for the damage initiation/fracture model in the equivalent plastic strain-stress triaxial space. The stress concentration exponent m was calibrated by a uniaxial tensile test by using different sizes of a virtual extensometer. At last, the model parameters are validated through a stretch bending test. The comparison of the experimental and FE simulation results demonstrates that the new coupled mesh size effect fracture model can predict stainless steel ductile fracture modelled by large sizes of shell elements with satisfactory accuracy.

Calibration of the modified Mohr-Coulomb fracture model by use of localization analyses for three tempers of an AA6016 aluminium alloy

This paper presents a novel calibration procedure of the modified Mohr-Coulomb (MMC) fracture model by use of localization analyses and applies it for three tempers of an AA6016 aluminium alloy. The localization analyses employ the imperfection band approach, where metal plasticity is assigned outside the band and porous plasticity is assigned inside the band. Ductile failure is thus assumed to occur when the deformation localizes into a narrow band. The metal plasticity model is calibrated from notch tension tests using inverse finite element modelling. The porous plasticity model is calibrated by use of localization analyses where the deformation histories from finite element simulations of notch and plane-strain tension tests are prescribed as boundary conditions. Subsequently, localization analyses are used to establish the failure locus in stress space for proportional loading conditions and thus to determine the parameters of the MMC fracture model. Finite element simulations of notch tension and in-plane simple shear tests as well as two load cases of the modified Arcan test are used to validate the calibrated fracture model. The predictions by the simulations are in good agreement with the experiments, even though some deviations are seen for each temper. The results demonstrate that localization analyses are a cost-effective and reliable tool for predicting ductile failure, reducing the number of mechanical tests required to calibrate the MMC fracture model compared to the hybrid experimental-numerical approach usually applied.

A study of Inconel 718 dependency on stress triaxiality and Lode angle in plastic deformation and ductile fracture

A numerical and experimental study of monotonic tensile tests on Inconel 718 with different stress states has been investigated. Focus was put to dependencies of stress triaxiality and Lode angle parameter on plastic behavior and ductile fracture. The constitutive plasticity model proposed by Bai and Wierzbicki (2008) and the modified Mohr–Coulomb (MMC) ductile fracture model (Bai and Wierzbicki, 2010) were adapted with suitable extensions. Experimental results were used to calibrate the models. By setting up parameter optimization for model calibration, the experimental results and numerical simulations were well correlated. Finally, the MMC fracture model well predicted both fracture initiation and fracture propagation modes.

Experimental and numerical study on the plane-strain blanking process on an AHSS sheet

The blanking/trimming/cropping process introduces a substantial plastic deformation to the sheet metal and causes premature edge fracture during the subsequent forming process. In an attempt to understand how the blanking process affects edge fracture, an experimental and numerical study was undertaken on the plane-strain blanking process. Blanking tests on a DP780 steel sheet were carried out on a special fixture utilizing a in-situ microscope for the digital mage correlation (DIC) deformation measurement. The DIC method provides a detailed deformation field of the specimen that has not been reported in any other publications before. Interrupted tests were carried out to study the crack formation and propagation during the blanking procedure, while scanning electron microscope was applied to examine the blanked surface quality as well as the edge profile after test. Following the experimental study, a detailed finite element model with mesh size of 0.01 mm in the critical region was established for the numerical investigation. The model features (a) a non-associated Hill 48 flow rule, (b) von-Mises yield condition and (c) modified Mohr–Coulomb fracture model. With material parameters calibrated from the in-plane tests as well as accurate boundary conditions measured in actual tests, the finite element model accurately predicted the blanking process quantitatively. The current study also gave quantitative values of the parameters of interest during the blanking test, such as the global load displacement response and the local strain gradient history. The geometrical features of the blanked edge, i.e. the amount of roll over, the extent of the burnished zone and fracture zone were all accurately predicted by the present simulation.

Experiments and modeling of edge fracture for an AHSS sheet

With the emergence of advanced high strength steels (AHSSs) and other light–weight materials, edge fracture has been one of the important issues evading reliable prediction using CAE tools. To study edge fracture behavior of AHSS, a comprehensive hole expansion test (HET) program has been carried out on a DP780 sheet. Specimen with three different edge conditions (milled edge, water jet cut edge and punched edge) are manufactured and tested. Results reveal that the hole expansion ratio (HER) of the present DP780 sheet is around 38 % for milled specimen and water jet cut specimen, and about 14 % for punched specimen. A novel method of a central hole specimen tension is also introduced for edge fracture study, showing a similar trend as found in HET. The paper briefly presents a procedure and the results for a full calibration of the DP780 sheet for plasticity and fracture, where a hybrid testing/simulation method is used to obtain parameters for Hill 48 plasticity model and modified Mohr–Coulomb fracture model. The finite element simulation gives an accurate prediction of HER, as well as the load displacement response and specimen deflection distribution in the hole expansion tests on uncracked material. The correlation between simulation and tests on central hole specimen also turns out to be very good. The paper also presents a very interesting insight of the initiation and propagation of cracks from the hole edge during a hole expansion test by numerical simulation in comparison with testing observation. The number of final cracks are accurately predicted. Other new aspects of the present paper include an improved 3D DIC measurement technique and a simplified analytical solution, from which a rapid estimation of displacement and hoop strain field can be made (see “Appendix 2”).

Fracture modelling of DP780 sheets using a hybrid experimental-numerical method and two-dimensional digital image correlation

This paper is concerned with the construction of fracture envelopes of DP780 sheets using two methods: a hybrid experimental-numerical method; two-dimensional digital image correlation (2D-DIC). For the hybrid method, four types of ductile fracture tests were carried out covering a wide range of stress states on specimens: with a central hole; two symmetric circular notches; flat grooved; and diagonally double-notched. Based on the fracture strain and loading paths identified with finite element simulation, a fracture envelope was obtained by employing the three-parameter modified Mohr-Coulomb fracture model. In addition, the fracture surface strain was directly measured using 2D-DIC. Loading histories of each test were extracted from a surface element of a three dimensional finite element model. The comparison of fracture envelopes constructed by the two methods reveals that there is little difference. Thus, it can be concluded that 2D-DIC is applicable to fracture modelling of DP780 sheets despite the assumption of the plane stress condition even after necking.

Numerical failure analysis of a stretch-bending test on dual-phase steel sheets using a phenomenological fracture model

Advanced High Strength Steels (AHSS) are increasingly used in automotive industry due to their superior strength and substantial weight advantage. However, their compromised ductility gives rise to numerous manufacturing issues. One of them is the so-called ‘shear fracture’ often observed on tight radii during stamping processes. Since traditional approaches, such as the Forming Limit Diagram (FLD), are unable to predict this type of fractures, great efforts have been made to develop failure criteria that could predict shear fractures. In this paper, a recently developed Modified Mohr–Coulomb (MMC) ductile fracture criterion ( Bai and Wierzbicki, 2010) is adopted to analyze the failure behavior of a Dual Phase (DP) steel sheet during stretch-bending operations. The plasticity and ductile fracture of the present sheet are fully characterized by a Hill’48 orthotropic model and a MMC fracture model, respectively. Finite element models with three different element types (3D, shell and plane strain) were built for a Stretch Forming Simulator (SFS) test ( Shih and Shi, 2008), numerical simulations with four different R/ t values (die radius normalized by sheet thickness) were performed. It has been shown that the 3D and shell element simulations can predict failure location/mode, the upper die load–displacement responses as well as wall stress and wrap angle at the onset of fracture for all R/ t values with good accuracy. Furthermore, a series of parametric studies were conducted on the 3D element model, and the effect of tension level (clamping distance), tooling friction, mesh size and fracture locus on failure modes and load–displacement responses were investigated.

Partially coupled anisotropic fracture model for aluminum sheets

The objective of the present paper is to incorporate the effect of plastic anisotropy on the fracture modeling of aluminum alloy 6061-T 6 sheets. Six different types of tests were performed to fracture, including tensile tests on classical dog-bone specimens, flat specimens with cutouts, plane strain grooved specimens, and punch indentation tests on circular blanks. A limited number of shear/tension tests on butterfly specimens were performed on a dual-actuator loading frame. Plastic properties were determined from the dog-bone tensile tests, and were verified by the remaining tests. It was found that the sheets exhibited little planar anisotropy but substantial out-of-plane anisotropy, characterized by the Lankford parameter, r. A comprehensive numerical analysis of the experiments revealed that the Hill 1948 quadratic anisotropic yield model is able to describe, with good accuracy, the plastic response of all five types of tests. Fracture surface strains were measured using a digital image correlation system. Average fracture strains were determined by measuring post-fracture thickness reduction. Local fracture strains were determined by means of an inverse engineering method involving matching the displacement to fracture from numerical simulations to those measured. Possible discrepancies between the magnitudes of the fracture strain in the three above methods are discussed. Based on the previous experience of the investigating team, the experimental fracture data were analyzed within the realm of the three-parameter Modified Mohr–Coulomb fracture model. Using the plane stress anisotropic plasticity equations, the calibrated fracture model was then transformed to the space of the equivalent strain to fracture and stress triaxiality. An alternative representation of the fracture locus in the space of principal strains was also constructed. Other important factors influencing the form of the fracture locus, such as mesh-size effect and solid versus shell representation, were also investigated.